Analysis of a High Phase Self Excited Induction Generator

M. Faisal Khan, Member IEEE

Electrical Engineering Section, University Polytechnic Faculty of Engg. & Technology, Aligarh Muslim University

Aligarh-202002, India mfaisal_khan@yahoo.com

M. Rizwan Khan, Member IEEE

Electrical Engineering Department, Zakir Husain College of Engineering & Technology, Aligarh Muslim University,

Aligarh - 202002, UP, India rizwan.eed@gmail.com

Abstract— High (more than three) phase self excited induction generators (SEIGs) are evoking lots of interest amongst researchers off late. This may be attributed to better stability and reliability of these machines in general. This paper presents the study of a six phase self excited induction generator (6Ph-SEIG) operating with optimum excitation capacitances. For this purpose detailed mathematical modeling of a six phase SEIG and its implementation in simulink is achieved. Extraction of magnetizing characteristic and evaluation of optimum excitation capacitance are explained through conducted experimental investigation. The paper is concluded by reporting no-load voltage profile of six phase SEIG in the present case. An open stator winding, 2.2 KW induction machine connected for six phase operation is utilized for the analysis.

Keywords- high phase SEIG, magnetizing characteristic, synchronous speed test, excitation capacitance, no-load voltage.

Nomenclature

I. INTRODUCTION One of the most important advancements in field of

electrical machines in recent past is the development of high phase (more than three phase) technology. High-phase machines offer compact unit size, increased power output, better stability, less torque ripples and the reduced acoustic noise over their equivalent rating three phase variants [1]-[4]. High-phase SEIGs combine the ruggedness and maintenance free properties of SEIGs with the high phase technology to yield an extremely useful generating machine.

Steady state analysis of six phase self excited induction generator is pursued by a number of reported works [5]-[7]. Genetic Algorithm (GA) based analysis is proposed in [5]. The analysis presented in [6] consideres different types of loads and excitation configurations in the steady state model. In [7] the steady state analysis of a dual stator winding SEIG is reported through a MATLAB based tool “FZERO”.

Although, steady state analysis renders useful

explanation on performance of SEIGs it does not yield dynamic behavior. The dynamic model is capable of yielding steady as well as transient state behaviors of investigated machine. One of the earliest dynamic models for a high phase order induction machine was developed by Nelson [8]. Later on Lip [9] provided a detailed insight into the model of dual stator winding induction machine for six phase application to devise a method for estimating slot mutual leakage inductance, Llm between two three phase windings. An alternate approach for the modeling of six phase SEIG is proposed by Duran in [10] which is based on space vector decomposition theory [11] wherein a six phase-SEIG is modeled in terms of fixed winding placement of 60 degrees (electrical) to get a composite six phase winding.

Both modeling approaches are equally viable in terms of

implementation and analysis. However, the dual stator winding approach offers more flexibility of operation. Besides the freedom of arbitrary angle of displacement between winding sets, the respective neutrals of two sets of winding may be isolated from each other or connected together. The isolated neutral electrically separates two winding sets thereby avoiding circulation of faults from one set to another [12].

Symbol Description Rs ,Rr, RL stator, rotor and load resistances (ohms) Lsl ,Lrl, Llm stator & rotor leakage inductances (henry) Ψsd,Ψsq d and q axes stator flux(wb) Ψrd,Ψrq d and q axes rotor flux(wb) Ψrd0, Ψrq0 d and q axes initial rotor flux(wb) vdcap1,2, vqcap1,2 d and q axes instantaneous voltages across

excitation capacitances of winding sets ABC(subsc_1) and XYZ(subsc_2) (volts).

V0dcap1,2 V0qcap1,2 d and q axes voltages due to initial charge on excitation capacitances of ABC and XYZ winding sets (volts).

idcap1,2, iqcap1,2 d and q axes capacitor currents(amps) isd, isq d and q axes stator currents(amps) ird, irq d and q axes rotor currents(amps) iLd1,2, iLq1,2 d and q axes load currents of winding sets

ABC and XYZ(amps) ωr rotor electrical speed(rads/sec) Lm magnetizing inductance (henry) IL load Current(amps) Is stator current(amps) Im magnetizing current(amps) Po active power generated (watts) Qc reactive power (var) Cex per phase excitation capacitance(µF) ωr rotor electrical speed(rads/sec) Ψm magnetizing flux (wb) vdr0, vqr0 d and q axes rotor induced voltages due to

remnant flux(volts) Xex reactance of capacitance reactance(ohms)

In this paper a detailed experimental and analytical study of 6Ph-SEIG is carried out to evaluate its optimum excitation capacitance and analyze no-load characteristics. A detailed dynamic model of 6Ph-SEIG in dual stator winding configuration is developed in stationary reference frame and implemented in terms of a simulink model through Matlab.

II. MATHEMATICAL MODELING AND SYSTEM DESCRIPTION

The modeling approach for 6Ph-SEIG adopted in this study is an extension of that adopted in [13] for the modeling of 3 phase SEIG in stationary reference frame. For this purpose the circuit model of d and q axes of a 6Ph-SEIG incorporating various flux linkages between passive elements is illustrated in Fig. 1 [8],[9],[14] which is yielded by the fundamental flux linkages of a dual stator winding SEIG formulated in [8],[9],[14]. The circuit model of d-q axes circuits shown in Fig. 1 can be represented by a state space equation given by (1)

Figure 1. d-q model of a 6Ph-SEIG in stationary reference frame.

ωr[K][i]T+[L]p[i]T+[v]T=0 (1) Where,

[v] = [vqcap1 vdcap1 vqcap2 vdcap2 vqr0 vdr0] [i] = [isq1 isd1 isq2 isd2 irq ird]

[L]=

⎣⎢⎢⎢⎢⎡Llm+Ls1 0 Llm+Lm 0 -Lm 0

0 Llm+Ls1 0 Llm+Lm 0 -LmLlm+Lm 0 Llm+Ls2 0 -Lm 0

0 Llm+Lm 0 Llm+Ls2 0 -Lm-Lm 0 -Lm 0 Lr 0

0 -Lm 0 -Lm 0 Lr ⎦⎥⎥⎥⎥⎤

;

[K]= ωr

⎣⎢⎢⎢⎢⎢⎡Rs1/ωr 0 0 0 0 0

0 Rs1/ωr 0 0 0 00 0 Rs2/ωr 0 0 00 0 0 Rs2/ωr 0 00 Lm 0 -Lm Rr/ωr -Lr

-Lm 0 -Lm 0 Lr Rr/ωr⎦⎥⎥⎥⎥⎥⎤

Ls1= Lls1+Lm ; Ls2= Lls2+Lm; Lr= Lrl+Lm ; vqr0 = -ωrΨqr0 ; vdr0 = ωrΨdr0 Solving For currents, (1) is re-written as: p[i]T = −[L]-1ωr[K][i]T − [L]-1[v]T (2) p=d/dt. The modeling of different SEIG parameters is given as: Modeling of Excitation Capacitance:

vqcap1= 1

Cex iqcap1 dt+ V0qcap1

vdcap1= 1

Cex idcap1 dt+ V0dcap1

vqcap2= 1

Cex iqcap2 dt+ V0qcap2

vdcap2= 1

Cex idcap2 dt+ V0dcap2

(3)

Here, iqcap1=isq1 ; idcap1=isd1. ; iqcap2=isq2. ; idcap2=isd2. The SEIG currents are yielded by (2) and the no-load d-q axes currents for dual stator windings are given by (3).

III. EVALUATION OF MAGNETIZING CHARACTERISTIC The magnetizing characteristic of 6Ph-SEIG in the present

case is evaluated through synchronous speed test [15,16]. In order to secure six phase supply mains a 3ph-to-6ph, 400 V/ 114 V transformer is employed. Moreover, to step up the secondary line voltage up-to motor rating 400 V from 114 V, 6 auto-transformers in each of the six phases of transformer are accommodated in series and connected in reverse order with respect to their input and output. The SEIG is then supplied 6-phase power from this customized system and driven simultaneously by the prime mover at a constant speed of 1500 rpm i.e., the rated speed of SEIG. The direction of rotation of SEIG from prime mover and the revolving field due to six phase supply must be same. Subsequent to collecting the requisite data from the test the variation of Lm i.e., magnetizing inductance with per phase no-load voltage applied to energize the stator winding is formulated in terms of (4). Lm= p1*Vph^4+p2*Vph^3+p3* Vph^2 + p4*Vph+ p5. (4) p1 = -2.8962e-009, p2 = 1.5397e-006, p3 = -0.00025066, p4 = 0.0075207, p5 = 1.9922.

Figure 2. 3ph-to-6ph transformer arrangement along with necessary

autotransformers to get 6 phase rated output voltage of 400 V.

IV. DESCRIPTION OF EXPERIMENTAL SET-UP An open stator winding multi phase squirrel caged

induction machine is deployed as SEIG for the analysis. The Excitation capacitances are placed as a double Y connected bank having conjoined neutrals. The neutral points of SEIG and excitation capacitance bank are tied to a common ground available in the laboratory. A 3ph, 3.7 KW induction motor is utilized as prime mover controlled by a Yaskawa AC inverter drive for constant speed operation. The 6Ph-SEIG test rig is shown in Fig. 3 while detailed equipment parameters are given in Appendix I.

1.Inverter Drive, 2.Prime Mover, 3.Open Stator Winding SEIG, 4.Excitation Capacitances, 5. DSOs.

Figure 3. 6Ph-SEIG Test Rig.

V. RESULTS AND DISCUSSION

Variation of no-load voltage of 6Ph-SEIG with excitation capacitance and speed is illustrated in Fig. 4. An optimum excitation should establish rated no-load voltage across the SEIG terminals when it is driven at the rated speed. Considering the given criteria it can be clearly seen from Fig. 4 that in present case an excitation capacitance of 4µF sets-up rated no-load voltage at 1500 rpm. Thus, from the plotted characteristic an optimum excitation capacitance is evaluated as 4 µF for the 6Ph-SEIG under investigation.

Figure 4. Measured variation of no-load voltage generated of 6Ph-SEIG with

speed and excitation capacitance. Phase A voltage build-up of 6Ph-SEIG recorded on a power scope is illustrated in Fig. 5(a). To obtain this result the SEIG windings are connected with the star connected bank of optimum excitation capacitances. The SEIG speed is then built up-to the rated value of 1500 rpm through prime mover excited from the speed controller. The voltage starts to appear across the out-put terminals at a speed of 1200 rpm. Afterwards, the voltage increases rapidly and as the rated speed of 1500 rpm is achieved the machine saturates to establish steady state no-load voltage of 230 V. The corresponding simulated result obtained from the simulink model is depicted in Fig. 5(b). The simulink model developed from the 6Ph-SEIG mathematical model described from (1) to (3) in conjunction with its magnetizing characteristic evaluated by (4) as well as the six phase winding configuration are illustrated in Appendix-II.

(a)

(b)

Figure 5. Phase A no-load voltage build-up achieved with optimum excitation capacitance of 4 µF and 1500 rpm (a) recorded (b) simulated.

3 3.5 4 4.5 5 5.5 6140

160

180

200

220

240

260

280

300

Cex(µF)

VN

L (v

olts

)

1400 1450 1500 1550 1600 1650 1700140

160

180

200

220

240

260

280

300

320

Speed (rpm)

VN

L(v

olts

)

VNL vs Speed

VNL vs Cex

0 1 2 3 4 5 6 7 8 9 10-400

-300

-200

-100

0

100

200

300

400

Time(sec)

V NL

(Vol

ts)

2

1

3

4 5

The no-load voltages of all six phases of SEIG are simultaneously recoded on a YOKOGAWA power scope to provide a consolidated view of generated voltages. The recorded and simulated results are shown in Fig. 6(a) and Fig. 6(b) respectively. It can be seen that all the six phase generated voltages are balanced.

(a)

(b)

Figure 6. Zoomed view of No-load voltages all six phases of SEIG with optimum excitation capacitance of 4 µF and 1500 rpm (a) recorded (b) simulated.

The Three winding set excitation scheme is also

investigated to estimate the performance deviations of SEIG. For this mode of operation either ABC or XYZ winding set is excited from a bank of three optimum capacitances connected in star while the other winding set is left unexcited. Such a winding scheme facilitates generation of no-load voltage of 230 V per phase in the three excited windings at the rated input speed of 1500 rpm. However, the unexcited windings have about 160 V induced in them per phase i.e. about 70% of rated no-load voltage. This is true irrespective of whether winding set ABC is excited and XYZ is kept open or vice-versa.

VI. CONCLUSION Dynamic modeling and analysis of a high (six) phase SEIG is carried out to evaluate optimum excitation capacitance. The procedure for extracting magnetizing characteristic is explained and the magnetizing characteristic of investigated machine is reported in the paper. For the investigated machine

an excitation capacitance of 4 µF is found to be optimum as it establishes rated no-load voltage of 230 V per phase at rated speed of 1500 rpm in the six phase SEIG windings. The simulation results are obtained through a simulink model of six phase SEIG developed for the purpose. The experimental validation of the simulated results is achieved through a 2.2 KW, 400 V, open stator winding induction machine.

Appendix I

Parameters of Prime Mover 3-phase, Delta connected, 415 V, 7.6 A, 3.7 KW, 1430 rpm, 50 Hz, Squirrel caged induction motor.

Parameters of SEIG Open stator winding, star connected, squirrel caged, 3 hp, 400 V, 2.5 A, Rs1= Rs2=10.3 Ω, R’r=7.6 Ω, Lls1= Lls2 L’lr=0.040,Llm=0.001. Parameters of Inverter Drive (Speed Controller) Yaskawa V1000 AC Drive, 3phase, 2.2 KW, 400V.

APPENDIX II

Y,4

B, 3C, 5

Z, 6 X, 260o

A, 160o

60o

60o60o

60o

Figure 7. Six phase SEIG winding configuration.

Figure 8. Simulink model of six-phase SEIG

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3.03 3.035 3.04 3.045 3.05 3.055 3.06 3.065 3.07 3.075 3.08-400

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isd1

isq2

isd2

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